Measuring Hicksian Welfare Changes from Marshallian Demand Functions

A problem persists in measuring the welfare effects of simultaneous price and income changes because the Hicksian compensating variation (CV) and equivalent variation (EV), while unique, are based on unobservable (Hicksian) demand functions, and observable (Marshallian) demand functions do not necessarily yield a unique Marshallian consumer's surplus (CS). This paper proposes a solution by a Taylor series expansion of the expenditure function to approximate CV and EV by way of the Slutsky equation to transform Hicksian price effects into Marshallian price and income effects. The procedure is contrasted with McKenzie's "money metric" (MM) measure derived from a Taylor series expansion of the indirect utility function. MM requires a crucial assumption about the marginal utility of income to monetize changes in utility levels. No such assumption is required by the proposed procedure because the expenditure function is measured in money units. The expenditure approach can be used to approximate EV and CV while the MM is an approximation to EV. The EV and CV approximations are shown to be very accurate in numerical examples of two prices and income changing simultaneously, and are generally more accurate than MM.